# Competing Risks

Competing risks is a specialized topic in statistical methodology. It is used for analyzing time-to-event data. In people diagnosed with oral cancer, there are two possible events: death from cancer and death from other causes. In this type of analysis, what is observed is the single cause of death that occurs first.

Competing risks survival is different from the analysis of single causes of death, which may be an analysis of all causes of death or of a single cause of death (e.g. cancer) under a hypothetical assumption that other causes of death cannot occur. The latter analysis is useful when the focus is solely on the chance of cancer death, removing the confounding effects of the chance of other-cause death. For example, we may be interested in improvements in 5-year survival by year of diagnosis for a specific cancer, but do not want to have these changes influenced by improvements in death from causes other than the cancer of interest.

We have used the competing risks method to produce the estimates for this calculator. This calculator takes into account both factors associated with the chance of death from cancer and factors associated with the chance of death from other causes. Many methods have been developed for analyzing competing risks. For this calculator, we have used adaptations of the method first developed by Cheng et al. (1). Lee et al (2) modified the Cheng et al methodology (1) to permit two different time scales to be used for modeling the effects of the outcomes of interest, as opposed to modeling them both on the same time-to-event scale. This makes sense because generally we think of the risk of death from cancer in terms of time from diagnosis, and the risk of death from other causes in terms of age. Lee’s methodology enabled simultaneous modeling of both time scales—as a function of risk factors associated with death from cancer and from other causes, respectively. Lee et al. (3) further modified Lee et al. (2) to utilize discrete rather than continuous time. This approach is particularly useful for cancer registry data where, because of confidentiality considerations, survival is calculated in whole months only, and the large samples sizes result in many ties between times to death and censoring (alive at the time of last follow-up). These ties are best accommodated by modeling that uses discrete time intervals.

Lee et al. (4) further refined the methods and allowed us to stratify the analyses differently for each outcome. For example, stage of disease is the most important prognostic factor for cancer death, so we stratified the analysis by stage. For other causes of death, sex is the most important factor, so we stratified the analysis by sex. Lee et al. also clarified how to conduct the modeling if each cause of death was modeled using independent or using partially overlapping data sources. All of these modifications gave us the flexibility to model competing risks in novel ways that take advantage of available data, the complexity of the risk factors, and their association with the risk of the two event types: cancer deaths and other-cause deaths.

### References

1. Cheng SC, Fine JP, Wei LJ. Prediction of cumulative incidence function under the proportional hazards model. Biometrics. 1998 Mar;54(1):219-28.
2. Lee M, Gouskova NA, Feuer EJ, Fine JP. On the choice of time scales in competing risks predictions. Biostatistics. 2017 Jan;18(1):15-31.
3. Lee M, Feuer EJ, Fine JP. On the analysis of discrete time competing risks data. Biometrics. 2018 Dec;74(4):1468-1481.
4. Lee M, Feuer EJ, Wang Z, Cho H, Zou Z, Hankey BF, Mariotto AB, Fine JP. Analyzing discrete competing risks data with partially overlapping or independent data sources and nonstandard sampling schemes, with application to cancer registries. Stat Med. 2019 Dec 20;38(29):5528-5546.